Question

Andre, Melissa, May, Robert, and Victor are each trying to sell a used car. The quality (q) of each seller's car is a result of the vehicle's driving, service and accident histories.

Seller	Andre	Melissa	May	Robert	Victor
q	4	3	2	1	0

Each seller knows the quality of his/her own car (because he/she knows the history), and values his/her car at an amount V = 1000 x q. Sellers will not accept a price that is less than their respective valuations.

Each buyer's willingness-to-pay for a car is WTP = 1500 x q. However, buyers cannot observe the quality of a given car. Therefore, buyers decide whether or not to purchase based on the average quality of the cars they believe to be in the market (it is assumed that the buyers are risk-neutral).

a) Calculate the value that each seller places on his/her car.

b) What is the average quality of the cars offered for sale if all five sellers participate in the market?

c) What is a buyer's maximum willingness to pay if all five sellers participate in the market?

d) Does the market unravel? Explain. [Hint: Would every seller accept the highest price buyers are willing to pay? What happens to your answers to parts (b) and (c) if a seller drops out of the market?]

e) Propose at least TWO (2) practical solutions to overcome the problem revealed in this question.   

Answer 1

a) Seller's valuation is 1000*q.

So for Andre, the valuation is 1000*4=$4000

For Melissa , it is 3*1000= $3000

May, the value of the car is 1000*2=$2000

Robert:1000*1= $1000

Victor: 1000*0= $0

b) If all 5 sellers are there in the market, then the quality would be (4+3+2+1+0)/5= 2

The average price of the car if all 5 sellers participate is $2*1000=$2000

c) Buyers maximum willigness to pay would be the average quality multiplied by 1500. Hence his average willingness would be $1500*2= $3000

d) the maximum willingness to pay for the buyer is $3000 which would not be accepted by only one seller. Other than that all would be willing to accept the price.

If the seller whose q=0, drops out of the market, the marginal willingness to pay by the buyer would increase, but the seller with th highest quality would still not be able to sell at his price.

Similarly if the seller with q=4 decides to opt out of the market, the price would reduce and the seller with q=3 would not be able to sell his car.

e)Two ways to let the information about the quality of car be known buyer is by

1) Seller having a warranty or guarantee of the car would help ensure the buyer about the quality of car and hence reduce the information barrier.

2)Mandatory information disclosure by seller could be another thing that could be done to reduce the problem of asymmetric information.